Asymmetry theory and the laws of thermodynamics at the quantum scale
Asymmetry provides a rigorous setting to characterise the different types of symmetries that can appear in a quantum system and quantify to what extent and how they can be broken. Quantum thermodynamics and reference frames are two special cases of the resource theory of asymmetry.
The ability to generate and manipulate quantum states to perform specific computational tasks lies at the heart of quantum information theory. One ubiquitous and important question in the field is: What are the necessary and sufficient conditions that characterise state transitions under a particular class of operations? During my PhD project I will address the more general scenario for state conversion under an arbitrary symmetric dynamics from a resource theoretic perspective. Further work will focus on the connections with thermodynamics and entanglement theory as well as extensions of Noether’s theorem to mixed states and applications to quantum information processing tasks.
A broader goal will be to develop the structural framework that describes quantum operations under symmetry constraints and generalise it to tensor networks in order to gain insights into how a global invariance breaks down locally via gauge degrees of freedom. This would provide a description of how asymmetry related quantum resources flow and are exchanged within many-body systems.